ABCD is a quadrilateral. A circle is drawn passing through B, C and D with centre A. If angle C is 100° then angle A will be?
Answers
Given:- In a circle ABCD is a quadrilateral having center A
To Prove:- angle CBD + angle CDB = 1/2 angle BAD
Construction:- Join AC and BD
Proof:- Since arc DC subtends angle DAC at center and angle CBD at a point B in the remaining part of the circle.
Thus, angle DAC = 2 angle CBD ....(i)
In a circle, the angle subtended by an arc at the center is twice the angle subtended by it at the remaining part of the circle.
Similarly, arc BC subtends angle CAB at center and angle CDB at a point D in the remaining part of the circle.
Thus, angle CAB = 2 angle CDB ....(ii)
In a circle, the angle subtended by an arc at the center is twice the angle subtended by it at the remaining part of the circle.
On adding equations (i) and (ii),
angle DAC + angle CAB= 2 angle CBD + 2 angle CDB
angle BAD = 2(angle CBD + angle CDB)
Given:- In a circle ABCD is a quadrilateral having center A
To Prove:- angle CBD + angle CDB = 1/2 angle BAD
Construction:- Join AC and BD
Proof:- Since arc DC subtends angle DAC at center and angle CBD at a point B in the remaining part of the circle.
Thus, angle DAC = 2 angle CBD ....(i)
In a circle, the angle subtended by an arc at the center is twice the angle subtended by it at the remaining part of the circle.
Similarly, arc BC subtends angle CAB at center and angle CDB at a point D in the remaining part of the circle.
Thus, angle CAB = 2 angle CDB ....(ii)
In a circle, the angle subtended by an arc at the center is twice the angle subtended by it at the remaining part of the circle.
On adding equations (i) and (ii),
angle DAC + angle CAB= 2 angle CBD + 2 angle CDB
angle BAD = 2(angle CBD + angle CDB)